L2 C4 S4
S4: The Gender Distribution of Children in a Family with Five Children
To see how these concepts can be applied in real world, we consider the following problem:
Suppose there are 1,000 Families in Gujranwala with exactly 5 children. Approximately how many families have 1 son and four daughters?
When children are born, they have about 50% chance of being male or female. Thus we can think of each child as a Bernoulli Trial which has outcome 1 for son and 0 for daughter. A family with 5 children has five Bernoulli RV's B1, B2, ..., B5. We can compute the probability of exactly 1 son as follows:
There are 5 outcomes: 10000, 01000, 00100, 00010, 00001 : each of the outcomes has probability 1/32, so the total probability is 5/32=15.6%. In a large sample, we would expect approximately 156 families to have exactly 1 son.
Question: How many families will have all five daughters?
Answer: Approximately 3.1% or 31 families. SHOW
Question: How many families will have exactly 3 sons?
Use the formula in previous slide to find out
True/False with EXPLANATION:
1. If the number of families with five daughters is 25, this means that the Bernoulli model is wrong, because there should be 31 such families.
2. List reasons why the Bernoulli model may fail to be an accurate representation of reality.